Sharpening the Becker-Stark Inequalities
© L. Zhu and J. Hua 2010
Received: 3 April 2009
Accepted: 14 January 2010
Published: 20 January 2010
In this paper, we establish a general refinement of the Becker-Stark inequalities by using the power series expansion of the tangent function via Bernoulli numbers and the property of a function involving Riemann's zeta one.
Theorem 1.1 (see [1, Lemma ]).
In fact, we can obtain the following further results.
In this paper, in the form of (1.2) and (1.3) we shall show a general refinement of the Becker-Stark inequalities as follows.
2. Four Lemmas
Lemma 2.2 (see [5, Theorem ]).
Lemma 2.3 (see [6, 22.214.171.124 (1.3)]).
3. Proofs of Theorems
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